Twirl¶
-
class
trueq.Twirl(twirl=None, labels=None)¶ A dictionary-like container mapping qubit labels to the corresponding twirling groups. Twirls are used in benchmarking protocols, e.g. cycle benchmarking (CB) and k-body noise reconstruction (KNR), or in randomized compiling (RC) to generate random twirling gates from specific groups in order to create dressed cycles.
Currently supported twirling groups are:
"P"(Pauli),"C"(Clifford),"U"(unitary), or"I"(identity). Warning:"I"is provided as a convenience method for expert users to identify coherent errors and/or crosstalk even though an exponential decay is not expected.The easiest way to initialize a twirl is to specify a twirling group and the labels on which this group will act on. This will result in a “homogenous” twirl, i.e. one that contains a single twirling group acting on all labels:
import trueq as tq tq.Twirl("C", (0, (1, 2)))
Twirl({(0,): 'C', (1, 2): 'C'})If you specify a single-qubit twirling group, e.g. Pauli, any multi-qubit labels passed to the constructor will be automatically broken up into single-qubit labels:
import trueq as tq twirl1 = tq.Twirl("P", (0, (1, 2))) twirl2 = tq.Twirl("P", (0, 1, 2)) twirl1, twirl2
(Twirl({(0,): 'P', (1,): 'P', (2,): 'P'}), Twirl({(0,): 'P', (1,): 'P', (2,): 'P'}))If you want to initialize a twirl with single-qubit Cliffords, regardless whether or not your cycle or labels contain multi-qubit gates, you can use the “C1” twirling group for convenience:
import trueq as tq tq.Twirl("C1", (0, (1, 2)))
Twirl({(0,): 'C', (1,): 'C', (2,): 'C'})A more explicit way of initializing a twirl is to pass it a dictionary mapping qubit labels to the corresponding twirling groups:
import trueq as tq tq.Twirl({0: "C", (1, 2): "C"})
Twirl({(0,): 'C', (1, 2): 'C'})Initializing a twirl with a dictionary allows you to specify “mixed” twirls, i.e. ones that contain multiple twirling groups acting on distinct labels:
import trueq as tq tq.Twirl({(0, 1): "C", (2, 3): "U", 4: "P"})
Twirl({(0, 1): 'C', (2, 3): 'U', (4,): 'P'})If you specify a permutation invariant twirling group, e.g. Clifford or U, the subsystem labels will be automatically sorted upon construction:
import trueq as tq twirl1 = tq.Twirl({(0, 1): "C", (2, 3): "U"}) twirl2 = tq.Twirl({(1, 0): "C", (3, 2): "U"}) twirl1, twirl2
(Twirl({(0, 1): 'C', (2, 3): 'U'}), Twirl({(0, 1): 'C', (2, 3): 'U'}))- Parameters
twirl (
dict|str) – Either a dictionary mapping qubit labels to the corresponding twirling groups or a string representing a single twirling group acting on all labels. IftwirlandlabelsareNone, then an empty twirl is instantiated.labels (
Iterable) – The labels on which the twirling group is acting on. Specify this only iftwirlis given astr.
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static
from_dict(dic)¶ Returns a
Twirlconstructed from a dictionary representation.- Parameters
dic (
dict) – A dictionary used to construct a new twirl.- Return type
-
property
groups¶ The set of all twirling groups in this twirl.
- Type
set
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property
is_mixed¶ Whether or not this twirl is mixed, i.e.
Trueif there is only one unique twirling group present (length ofgroupsis greater than one) orFalseotherwise.- Type
bool
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issubset(other)¶ Checks if this this twirl is a subset of another twirl.
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items()¶ Returns key-value pairs of this twirl.
- Return type
generator
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property
labels¶ The sorted union of all system labels in this twirl.
- Type
tuple
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labels_intersect(other)¶ Checks if any system labels in this twirl intersect with the labels of another twirl.
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pretty(max_chars=50)¶ Converts this twirl into a pretty string representation.
- Parameters
max_chars (
int) – The maximum length of the output.- Return type
str
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property
n_sys¶ The number of qubits in this twirl.
- Type
int
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to_dict()¶ Returns a dictionary representation of this twirl.
- Return type
dict